2011 International Conference on Computer and Software Modeling
IPCSIT vol.14 (2011) © (2011) IACSIT Press, Singapore
Image Security via Genetic Algorithm
Rasul Enayatifar a and Abdul Hanan Abdullah b
a
Department of Computer, Islamic Azad University, Firoozkooh Branch, Firoozkooh , Iran
b
Faculty of Computer Science & Information System, Universiti Teknologi Malaysia
Abstract. In this paper, a new method based on a hybrid model composed of a genetic algorithm and a
chaotic function is proposed for image encryption. In the proposed method, first a number of encrypted
images are constructed using the original image with the help of the chaotic function. In the next stage, these
encrypted images are employed as the initial population for starting the operation of the genetic algorithm. In
each stages of the genetic algorithm, the answer obtained from previous iteration is optimized so that the best
encrypted image with the highest entropy and the lowest correlation coefficient among adjacent pixels is
produced.
1. Introduction
With the ever-increasing growth of multimedia applications, security has become an important issue on
communication and storage of images. Usually, encryption is one better way to ensure the high security. It is
well-known that image encryption has extensively applications in Internet communication, multimedia
systems, medical imaging, telemedicine, and so on [1].
One of the proposed methods was the tree structure method in which the quad tree structure is selected to
be encrypted [2]. The advantage of such method was that it reduces the amount of time processing. The main
problem to this method was it was only suitable for the quad tree compression algorithm which is not an
international standard.
Another introduced method for image encryption was Cellular automata (CA) [3, 4]. A recent proposed
way is image encryption algorithm which can replace the pixel values in CBC-like mode by using recursive
CA [4].
It can be seen that a theory is exists in many research areas. This theory which is called Chaos theory has
many favorable usages for secure communication such as periodicity, sensitivity to initial conditions, control
parameters and random-like behavior. These features can be linked to the properties of a suitable cipher. Due
to the benefits of such a method, many scientists believe that this method can be a great help for image
encryption [5, 6]. Many researchers have found a close knit relation between chaos and cryptography [7,
8].Recently, an encryption method has been proposed which is based on a compound sequence [9]. This
scheme works in two ways; the first one deal with replacing the pixel values with XOR operations and the
second one deal with circular change in position of permutations in rows and columns.
In the proposed method, the chaotic function Logistic Map and a key extracted from the plain-image are
used to encrypt the image. The method mentioned is employed to produce a number of encrypted images
using the plain-image. These encrypted images are considered as the initial population for the genetic
algorithm. Then, the genetic algorithm is used to optimize the encrypted images as much as possible. In the
end, the best cipher-image is chosen as the final encryption image. In the rest of the paper, genetic algorithms
and chaotic functions are introduced, the proposed method is explained, and then experimental results and
the conclusions reached are presented.
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2. Chaootic Functtion
The chhaotic functiions are likee noise signals but they
y are compleetely certain, that is if we
w have thee
primary quaantities and the drawn function,
f
the exact amou
unt will be reproduced. T
The advantaages of thesee
signals will be as follow
ws: [10]
1) The
T sensitivityy to the prim
mary conditioons:
2) Thhe apparentlyy accidental feature:
3) Thhe Determiniistic work
The equuation (1) shhows one of the most fam
mous signalss which has chaotic
c
featuures and is known
k
as thee
logistic mapp signal.
X n +1 = rX
X n (1 − X n )
(1)
In whicch the willl get the num
mbers betweeen [0,1], thee signal show
ws three diffferent chaoticc features inn
three differeent range baased on the division
d
of thhe r parameter of which the signal feeature will be
b as well byy
consideringg the X0=0.3.
1) iff we have r € [0,3], then the
t signal feaature in the first
f
10 repetitions shhowed some chaos and affter that it waas fixed.
n the first 200 repetition showed som
me chaos andd
2) Iff we have r € [3, 3.57], then the signnal feature in
afterr that it was fixed.
f
3) Iff we have r € [3.57, 4], thhen the signaal feature is completely
c
chhaotic.
Accordiing to the giiven descripttion and the research req
quirements for
f the compplete chaotic features forr
image Encrryption, the logistic
l
map chaotic signnals with thee primary vallues of X0= 0.3and r € [3.57, 4], aree
used.
3. The proposed
p
Method
In ordder to form the
t initial poopulation froom the plain--image, first the plain-im
mage is divid
ded into fourr
equal parts, as shown inn Figure 1.
Fig 1: a) Plain-image
P
b) Plain-imag
ge divide to 4 equal parts
Then, thhe chaotic fuunction logisttic map is em
mployed to separately enccrypt all the pixels present in each off
these four parts
p
as follow
ws:
1- From
m each part of the image, five pixels are
a selected as
a the encrypption key for forming the initial valuee
of the Logiical Map fuunction and for
f encryptinng that part. The selection of thesee pixels is based
b
on thee
number of the
t populatioon being form
med. For exaample, if it is the first mem
mber of the ppopulation being
b
formedd,
then the firsst five pixelss of the first row are useed to form th
he initial valuue. If it is thhe second meember of thee
population being
b
formedd, then the fiirst five pixells of the seco
ond row are used
u
to makee the key, etcc.
2- The initial valuee of the chaootic functionn logistic map
p is determiined from thhe following equation byy
g
scales of the five pixxels.
using the vaalues of the gray
199
,
In whicch,
,
,
,
2
represeents an eightt- bit block. Then,
T
equatio
on 3 is used to
t convert P into an ASC
CII number.
,
,
,
,
,
,…,
,
,
,
,…,
,
,
3
,
After P is turned intto an ASCII number, thee string B wiith a length of
o 40 bits is produced. In
n equation 3,,
Pi, j stands for the
b of the
bit
block. Finally, by usin
ng equation 4, the initiaal value for starting thee
execution of the chaoticc function loggistic map is obtained.
,
2
,
2
,
2
,
2
,
2
2
1
1,2,3,4
4
In whicch, k is the number
n
of each part of thhe image (Fig
gure 1.b). Byy using this rrelation, the initial valuee
of the logisttic map function (U0k), which
w
lies in the
t interval 0 to 1, is obtaained.
3- For each
e
part off the plain-im
mage, step 2 is repeated.. Therefore, in the end, there will bee 4 differentt
initial valuees for each im
mage (one vaalue for each part of the image).
4- For encrypting
e
thhe pixels in each part off the image, the initial value
v
of that part and eq
quation 5 aree
used as folloows:
255
5
In equaation 5, the symbol reepresents XO
OR,
stands for the current value of th
he pixel, andd
NewValue shows
s
the neew value of the pixel aftter it is encry
ypted. The value
v
of
refers to the
value off
the chaotic function inn the
parrt of the oriiginal imagee, which is determined for each steep by usingg
equation 1.
All the pixels in eacch part, exceppt the 5 pixels used as thee key, are sequentially (rrow by row) encrypted inn
this way. Fiinally, the firrst member of
o the populaation is built by
b using the mentioned m
method.(Figu
ure 2)
To build thee rest of the population,
p
s
steps
1 through 5 are repeeated.
Fig 2: First genneration of gen
netic population
1.2 Genetiic Optimizattion
200
After forming the initial population, the genetic algorithm is used to optimize the encrypted images.
The genetic algorithm introduced in this study uses the crossover operation as shown in Figure 3. Figures 3.a
and 3.b show the input images for the crossover operation, and Figures 3.c and 3.d show these images after
the crossover operation.
Fig 3: a, b) Input images
c, d) Images after crossover
The fitness function used in this paper is the correlation coefficient between pairs of adjacent pixels of
the image. At each stage, the new generations produced and the previous ones are evaluated using the fitness
function and 50% of the population with the minimum correlation coefficient and 10% of the remaining
population is selected for the next generations. In each generation, the individuals which are not selected as
elites are not participating in reproduction in the entire algorithm, in spite of the fact that their combination
with the elites may result in better solutions, therefore, 10% of the remaining population are chosen
arbitrarily to help the selected 50% elites for production of the new generations. This process is repeated
until the correlation coefficient of the best generation produced does not significantly change in two
successive stages. After this stage, the generation which had the lowest correlation coefficient is encrypted as
the final cipher-image. The only important point here is that in each generation the number of populations
that generation is built must be maintained. In the end, the image having the lowest correlation coefficient
and the number of the population, or the numbers of the two populations, the image is made from are sent to
the destination.
4. Experimental Results
In this section, the efficiency of the proposed method in the different parts is introduced.
4.1 Image Entropy
Entropy is one of the prominent features in randomization. Information entropy is a mathematical
theory for data communication and storage introduced in 1949 by Claude E Shannon. Equation 6 is
introduced for obtaining entropy [11].
log
1
6
In which, N is the number of gray levels used in the image (for gray level images, N is 8), and ( )
shows the probability of having a
gray level in the image. In images that are produced in a completely
random way, N will be 8; which is considered as an ideal value. Our paper is shown entropy about 7.9978.
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4.2 Correlation coefficient
A good encryption algorithm is one in which the correlation coefficient between pairs of encrypted
adjacent pixels in the horizontal, vertical, and diagonal positions are at the least possible level. The
correlation coefficient is calculated by using equation 7.
|cov x, y |
7
D y
D x
In the above relation, x and y are the gray levels in two adjacent pixels of the image. In calculating the
correlation coefficients, the following equations are employed:
cov x, y
E x
D x
N
1
N
1
N
1
N
x
E x
y
E y ,
8
N
x,
9
N
x
E x
.
10
To test the correlation coefficient between two adjacent vertical pixels, two adjacent horizontal pixels,
and two adjacent diagonal pixels in a cipher-image, the following procedure is used: first, 2500 pairs of
pixels are randomly selected, and then the correlation coefficient is obtained by using equation7(the results
of which are shown in Table 1).
Table1. Correlation coefficient of two adjacent pixels in two images
Plain-Image
Cipher-Image
Vertical
0.9711
0.0093
Horizontal
0.9445
-0.0054
Diagonal
0.9217
-0.0009
4.3 Key analysis
A suitable encryption algorithm must be sensitive to small changes in keys. Moreover, the key must be
long enough to resist against brute-force attacks. In this study, a 40-bit long key is suggested which produces
a key space equivalent to 2 (and hence this key seems to be long enough).To test the sensitivity of the key
in the proposed method, first the Photographer image (Figure 4a) is encrypted using the proposed method
(Figure 4b). Then, this same image is encrypted once again using the proposed method, with the difference
that this time, in the stage of producing the initial population (when each member of the population is being
produced), one bit of the key of the member is changed; and the population is formed in this way. After this
new population is formed, the rest of the proposed method is executed, and in the end Figure 4c is obtained.
Figure 4d shows the similarity of the two encrypted images (the white points are the common points of the
two encrypted images). The two encrypted images are about 99.76% different.
5. Conclusions
In this paper, a new method has been suggested for encrypting images by using the chaotic function
logistic map and genetic algorithms. In this method, the chaotic function is employed for initial encryption
and the genetic algorithm is used to improve the encryption process of the image. The main innovation in
this paper is that this is the first time genetic algorithms are used in this way to encrypt images. Results
obtained for correlation coefficients and the entropies of the images also prove the high efficiency of this
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method, compared with other methods in image encryption. Moreover, this method, compared to other
methods mentioned in this paper, has a higher stability in the face of attacks common in this area.
Fig 4. (a) Plain-image, b,c) encrypted images using user keys with 1-bit difference in each parts; (d) the Similarity
between (b) and (c)
6. References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
X. F. Liao, S. Y.Lai and Q. Zhou. Signal Processing. 90 (2010) 2714–2722.
H. Cheng and X. Li. IEEE Transactions on Signal Processive. 48 (8) (2000) 2439–2451.
O. Lafe. Engineering Applications of Artificial Intelligence. 10 (6) (1998) 581–591.
R. J. Chen and J. L. Lai. Pattern Recognition. 40 (2007) 1621–1631
R. Enayatifar. Journal of the Physics Science. (2011) 221-228.
V. Patidar, N. K. Pareek, G. Purohit and K. K. Sud. Optics Communications, In Press, Corrected
Proof, Available online 26 May 2011.
S. Li, G. Chen and X. Zheng. Multimedia security handbook. LLC, Boca Raton, FL, USA: CRC Press; (2004)
[chapter 4].
Y. Mao and G. Chen. Handbook of computational geometry for pattern recognition, computer vision, neural
computing and robotics. Springer; (2003).
X. Tong and M. Cui. Image and Vision Computing. 26(6) (2008) 843–850.
H. S. Kwok, W. K. S. Tang, Chaos Solitons and Fractals, (2007) 1518–1529.
H. S. Kwok and W. K.S. Tang, Chaos Solitons and Fractals, (2007) 1518–1529.
203